Pairwise models are commonly used to describe many-species communities. In these models, a focal species receives additive fitness effects from pairwise interactions with other species in the community ('pairwise additivity assumption'), and all pairwise interactions are represented by a single canonical equation form ('universality assumption'). Here, we analyze the validity of pairwise modeling. We build mechanistic reference models for chemical-mediated interactions in microbial communities, and attempt to derive corresponding pairwise models. Even when one species affects another via a single chemical mediator, different forms of pairwise models are appropriate for consumable versus reusable mediators, with the wrong model producing qualitatively wrong predictions. For multi-mediator interactions, a canonical model becomes even less tenable. These results, combined with potential violation of the pairwise additivity assumption in communities of more than two species, suggest that although pairwise modeling can be useful, we should examine its validity before employing it.